How do you calculate deceleration due to resistance?

[cpalm]

I have a rocket with a top velocity of 14.16 m/s when the engine stops.

How do i calculate its deceleration based on air resistance and gravity if it is flying at approximatly 45 degress?

 

[Delphi51]

There is no easy way to deal with air resistance. It is ignored in most courses.
Also, we usually simplify matters by saying the engine burns for so small a time it is effectively zero.

So, it is just another baseball problem. Do the horizontal and vertical parts separately.

 

[nlightner]

To calculate deceleration due to resistance, we first need to understand the factors that contribute to resistance. In this case, we have air resistance and gravity acting on the rocket. Air resistance, also known as drag, is the force that opposes the motion of the rocket as it moves through the air. Gravity, on the other hand, is a constant force that pulls the rocket towards the ground.

To calculate deceleration, we can use the equation F = ma, where F is the total force acting on the rocket, m is the mass of the rocket, and a is the resulting acceleration. In this case, we can break down the total force into its components: the force of air resistance (Fdrag) and the force of gravity (Fg).

F = Fdrag + Fg

Since we know the top velocity of the rocket (14.16 m/s), we can use this information to calculate the force of air resistance using the equation Fdrag = 0.5 * ρ * A * v^2, where ρ is the density of air, A is the cross-sectional area of the rocket, and v is the velocity of the rocket.

Next, we need to calculate the force of gravity using the equation Fg = mg, where m is the mass of the rocket and g is the acceleration due to gravity (9.8 m/s^2).

Now, we can plug in these values into our original equation to calculate the total force acting on the rocket:

F = 0.5 * ρ * A * v^2 + mg

To calculate the resulting deceleration, we can rearrange the equation to solve for a:

a = (0.5 * ρ * A * v^2 + mg)/m

Since the rocket is flying at approximately 45 degrees, we can also take into account the component of gravity and air resistance acting in the vertical direction. This can be done by using trigonometric functions to calculate the vertical and horizontal components of these forces.

In summary, to calculate deceleration due to resistance, we need to consider the forces of air resistance and gravity acting on the rocket and use the equation F = ma to calculate the resulting acceleration. We can also take into account the angle of flight to calculate the vertical and horizontal components of these forces.